Article pubs.acs.org/Langmuir
Molecular Thin Films on Solid Surfaces: Mechanisms of Melting Haijun Feng,†,§ Kelly E. Becker,† Jian Zhou,§ and Kristen A. Fichthorn*,†,‡ †
Department of Chemical Engineering and ‡Department of Physics,The Pennsylvania State University, University Park, Pennsylvania 16802, United States § School of Chemistry and Chemical Engineering, South China University of Technology, Guangzhou 510640, China ABSTRACT: We use molecular dynamics simulations to study the melting of pentane and hexane monolayers adsorbed on the basal plane of graphite. For both of these systems, the temperature-dependent structures and the melting temperatures agree well with experiment. A detailed analysis reveals that a mechanism involving the promotion of molecules to the second layer underlies melting in these systems. In the secondlayer promotion mechanism, a small fraction of molecules transition into the second layer around the melting temperature, leaving vacant space in the first layer to facilitate disordering. The second-layer promotion mechanism arises because of the weaker molecule−surface interaction in our study than that in previous studies. The weaker molecule−surface interaction is consistent with experimental temperatureprogrammed desorption studies.
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We study n-pentane and n-hexane thin films on the basal plane of graphite at monolayer (ML) coverage for temperatures ranging from 0 K to melting. For the adsorption of n-pentane on graphite, our previous work26 indicated that the alkane− surface interaction is significantly weaker than that typically assumed in MD studies of alkane thin films. By adopting a proper alkane−surface interaction, our results agree with experimental scattering studies of the temperature-dependent structures and melting of these films. However, we find that the mechanism of melting, which involves the promotion of a small fraction of molecules to the second layer of the film, is qualitatively different than the footprint reduction mechanism16,21 typically invoked to explain melting in these systems. Our study emphasizes the importance of considering multiple experimental inputs in parametrizing force fields, particularly those for the molecule−surface interaction, for organic thin films.
INTRODUCTION Organic thin films have been heavily studied for applications such as thin-film transistors, solar cells, and light-emitting diodes.1−4 Although the structures of these films are of crucial importance in determining their performance, predicting and controlling organic thin-film structures is still a challenge. From a theoretical perspective, difficulties associated with handling large molecules and the significant role played by van der Waals interactions make first-principles studies challenging for many organic thin-film systems. Although some progress has been made in understanding organic thin-film structures using molecular dynamics (MD) simulations based on force fields,5−18 achieving sufficiently large system sizes and adequate simulation times can be challenging. Additionally, the reliability of the force fields for these simulations, especially those for the interaction of the molecules with the solid surface, can limit their capabilities. n-Alkane thin films are prototypical organic thin-film systems, and a great deal of theoretical11−18 and experimental19−25 effort has been directed toward understanding the low-temperature, solidlike structures and phase transitions in these systems. Theoretical efforts to understand the temperature-dependent structures measured in experimental scattering studies of these systems have shown that factors such as molecular flexibility, size, and small changes in coverage can play a significant role.11−18 Despite these efforts, the understanding of these systems is still not quantitative. In this work, we demonstrate that a quantitative description of the molecule−surface interaction, missing from previous studies of alkane thin films, is essential to capturing the temperature-dependent structures of these films. © 2012 American Chemical Society
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SIMULATION DETAILS We consider the melting of a monolayer (ML) of either npentane (C5H12) or n-hexane (C6H14) adsorbed on the basal plane of graphite C(0001). In our model,26−28 carbon and hydrogen atoms in the alkanes are treated explicitly, and the total energy Utotal is given by N
Utotal =
∑ Uintra,i + Uinter,i + Usurf,i i
(1)
Received: February 26, 2012 Revised: April 20, 2012 Published: April 23, 2012 7382
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where Uintra,i, Uinter,i, and Usurf,i are the intramolecular, intermolecular, and molecule−surface interactions for molecule i, respectively, and the sum runs over all N molecules. Intermolecular and intramolecular interactions are given by the OPLS-AA force field.29 We neglect Coulomb interactions because these are small for nonpolar alkane molecules. Because of their high stretching frequencies, we constrain C−C and C− H bond lengths to their equilibrium values. Similarly, we constrain H−C−H bond angles to their equilibrium values. In the MD simulations, we impose these constraints using the RATTLE algorithm.30 All other internal motions, including C− C−C and H−C−C bends and all torsions, are modeled explicitly. Thus, the intramolecular interactions for molecule i are given by Uintra, i = Uθ , i + Uφ , i + ULJ, i
σij =
Usurf, i =
(2)
V0(zj) =
+ V3j[1 + cos(3φj)]
⎛
p=0
6 2σjG
10 ⎝ 5(zj + pΔz)
−
⎞ 1 ⎟ (zj + pΔz)4 ⎟⎠
5 ⎤ 6 ⎡ 6 ⎛ ⎛ g ⎞2 2πεjGσjG σjG g1 ⎞ 1 ⎟ ⎢ ⎜ ⎟ ⎜ V1(zj) = K5(g1zj) − 2⎜ ⎟ K 2(g1zj)⎥ ⎥ as ⎢⎣ 30 ⎜⎝ 2zj ⎟⎠ ⎝ 2zj ⎠ ⎦
(10)
and ⎡ ⎛ 4πxj ⎞ ⎛ 2πxj ⎞ f1 (xj , yj ) = −2⎢cos⎜ − 2πyj ⎟ ⎟ + cos⎜ ⎝ 3 ⎠ ⎣ ⎝ 3 ⎠
(4)
⎞⎤ ⎛ 2πxj + cos⎜ + 2πyj ⎟⎥ ⎝ 3 ⎠⎦
where are the Fourier coefficients and φj is the dihedral angle for torsion j. In addition to bond-angle bending and torsion, nonbonded intramolecular interactions are important for atoms that are sufficiently far apart in the molecule. Nonbonded intramolecular interactions are given by a sum of Lennard-Jones (LJ) 12−6 pair interactions between all atoms j and k that comprise molecule i: Vj3
⎡⎛ ⎞12 ⎛ ⎞6 ⎤ σjk σjk = ∑ ∑ 4εjk ⎢⎢⎜⎜ ⎟⎟ − ⎜⎜ ⎟⎟ ⎥⎥f jk r ⎝ rjk ⎠ ⎦ j k>j ⎣⎝ jk ⎠
(11)
Here, the sum runs over all atoms j in molecule i, ε and σ are the energy and length parameters, respectively, for the alkane− surface interactions, G is graphite, as is the area of the graphite surface unit cell, Δz is the distance between graphite layers in the surface, Ki is a Bessel function of order i, and g1 is the magnitude of the first reciprocal lattice vector. The values of as, Δz, and g1 are taken from Steele’s paper.31 The expression for Usurf is terminated at V1, meaning that lateral corrugation in the potential is due to the first layer of carbon atoms only. We choose s = 1.5 to provide sufficient corrugation.32,33 Table 1 lists all of the parameters used in this article. All simulations in this study are run within the canonical (NρT) ensemble, where the number of molecules N, density ρ, and temperature T are constant. We use the velocity Verlet algorithm34 with a time step of 1 fs to integrate the equations of motion. Periodic boundary conditions are used in the two orthogonal directions parallel to the surface, and temperature control is implemented using the Berendsen thermostat.35
(5)
εjk and σjk are energy and length parameters, respectively. The factor f jk is added to turn off nonbonded interactions when two atoms are sufficiently close in the molecule that their interaction is governed by bond-angle bending or torsion. For 1−3 pairs (defined as third neighbors counting bonds along a connected path in the molecule) or less, f jk = 0; for 1−5 pairs (fifth neighbors in the molecule) and beyond, f jk = 1 and interactions between atoms in various segments in the molecule are the same as those between atoms in different molecules. Atoms pairs that are fourth neighbors in the molecule (1−4 pairs) have f jk = 0.5 by convention. Cross parameters for interactions between different atomic species i and j are calculated using Lorentz−Berthelot combining rules,
εiiεjj
as
∞
∑ ⎜⎜
(9)
where θj is the instantaneous bond angle, θeq,j is the equilibrium bond angle, and Kθj is the force constant for bond angle j. The torsion potential for molecule i is given by a sum over all its torsion angles as 1 Uφ , i = ∑ V1j[1 + cos(φj)] + V2j[1 − cos(2φj)] 2 j
εij =
6 4πεjGσjG
(3)
j
ULJ , i
(8)
where
j
Vj2,
∑ V0(zj) + sV1(zj) f1 (xj , yj ) j
∑ K θ (θj − θeq,j)2
Vj1,
(7)
2
The intermolecular interactions for molecule i are also given by a sum of LJ 12−6 pair interactions between all atoms j in molecule i and all atoms k in every other molecule. These can also be described by eq 5 with f jk = 1 for all pairs. The parameters and combining rules for intermolecular interactions are the same as those for nonbonded intramolecular interactions. A cutoff of 11 Å is used for intermolecular interactions. Interactions between the alkane molecules and the graphite surface are dominated by van der Waals forces and are modeled using a modified Steele potential.31,32 The molecule−surface interaction for molecule i is given by
Here, Uθ,i is the total bond-angle bending potential for molecule i and is given by a sum over all of its unconstrained bond angles as Uθ , i =
σii + σjj
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RESULTS AND DISCUSSION Low-Temperature Structures of the Ordered Layers. We first determined the ground-state structures for all-trans npentane and n-hexane MLs predicted by our model and compared them with those found in low-temperature neutron diffraction experiments.20,23−25 In determining these structures, we followed Hansen’s procedure16 to establish that the periodic
(6)
and 7383
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where a and b are the dimensions of the alkane ML unit cells, as indicated in Figure 1, na and nb are the corresponding (integer) numbers of alkane unit cells, a1 and a2 are the dimensions of the graphite unit cell (in the setup of Figure 1, a1 = a2 = 2.46 Å), and nx and ny are the (integer) numbers of graphite unit cells along the x and y directions, respectively. For pentane, with na = 12 and nb = 5 (i.e., 120 molecules), we have
Table 1. Parameters Used in Evaluating the Potential Energy Using Equations 3−10, Where C Is Carbon, H Is Hydrogen, and G Is Graphite parameter
value
Kθ (kJ/mol)
156.9 (C−C−H) 244.1 (C−C−C) 110.7 (C−C−H) 112.7 (C−C−C) 0.0 (H−C−C−H) 0.0 (H−C−C−C) 7.28 (C−C−C−C) 0.0 (H−C−C−H) 0.0 (H−C−C−C) −0.657 (C−C−C−C) 1.331 (H−C−C−H) 1.531 (H−C−C−C) 1.167 (C−C−C−C) 0.126 (H−H) 0.276 (C−C) 0.173 (C−G) 0.127 (H−G) 2.50 (H−H) 3.50 (C−C) 3.40 (C−G) 2.95 (H−G) 5.24 3.39 4π/31/2a1 2.46 1.5
θeq (deg) V1 (kJ/mol)
V2 (kJ/mol)
V3 (kJ/mol)
ε (kJ/mol)
σ (Å)
as (Å2) Δz (Å) g1 (Å−1) a1 (Å) s
xbox = a × 12 = 2.13nx
and ybox = b × 5 = 2.46ny
3 a1nx 2
Following previous work, we initially tried a = 4.67 Å and b = 17.01 Å, which leads to nx = 26.31 and ny = 34.57. Because nx and ny must be integers, we set nx = 26 and ny = 35, which leads to a = 4.62 Å and b = 17.22 Å. Using these values in the energy minimization of an all-trans pentane ML, we found a virtually uniform ML with one gap in the x direction. Excluding the gap, the distance between two nearest-neighbor pentane molecules in the x direction is 4.31 Å. Thus, we adopted a = 4.31 Å and b = 17.01 Å to recalculate nx = 24.28 and ny = 34.57, which we rounded to nx = 24 and ny = 35. The resulting pentane unit cell after energy minimization had dimensions of a = 4.26 Å and b = 17.22 Å, which eliminates the gap. To ensure that the resulting pentane ML was not compressed, we performed two different energy minimizations in which we deleted a whole row or a whole column of the ML, and we found that a and b remained virtually constant for the rest of the molecules (i.e., the ML did not expand). We also tried nx = 25 as well as ny = 36 and 37, but gaps formed in the ML with these integer values and the total energies were all higher than the ML with nx = 24 and ny = 35. Thus, it appears that pentane unit cell dimensions of a = 4.26 Å and b = 17.22 Å are reasonable for our model. For hexane, we used na = 4 and nb = 13 (i.e., 104 molecules), and we took initial values for a and b from Newton’s work.16,19,20 Following a similar procedure as for pentane, we found a = 17.04 Å and b = 4.92 Å for the hexane unit cell. The final ML unit cells are shown in Figure 1, where we see that pentane has a rectangular-centered (RC) arrangement and hexane has a herringbone (HB) structure. These ground-state
(12)
and
ybox = bnb = a 2ny
(15) 16,25
simulation boxes can hold integer numbers of both alkane unit cells and graphite unit cells. For a simulation box with dimensions of xbox and ybox, we have xbox = ana =
(14)
(13)
Figure 1. Schematic diagram of the ML unit cells for (a) pentane and (b) hexane. Each unit cell contains two molecules (1 and 2), and molecule 2 is in the center of the cell in panels a and b. The x and y axes are in the graphite [100] and [110] directions, respectively. 7384
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ML structures are commensurate with the graphite surface in both the x and y directions. Neutron and X-ray diffraction experiments have shown that both pentane23 and hexane19,20,24 MLs are uniaxially commensurate at low coverages and fully commensurate at high coverages. To characterize the ordered unit-cell structures further, we defined three angles specifying the molecular orientation, as shown in Figure 2, following the commonly used defini-
Table 3. Comparison of Experimental Lattice Values to Those Calculated in This Study for a Hexane ML at Zero Temperaturea 1 parameter
calc
x/Å y/Å Ψ/deg Θ/deg Φ/deg a/Å b/Å
0.00 0.00 −89.0 0.1 −62.7
2 20
calc
0.00 0.00 −90.0 0.0 −67.0
8.52 2.46 89.0 0.1 62.7
expt
lattice expt
20
calc
expt20
expt24
17.04 4.92
17.04 4.92
16.9 4.9
8.52 2.46 90.0 0.0 67.0
a
1 and 2 represent the two molecules in the unit cell (cf. Figure 1b). x and y denote center-of-mass coordinates. The lattice constants (a, b) and angles (Ψ, Θ, Φ) are defined in Figures 1 and 2, respectively.
unit cell and found a discrepancy of ∼9%. The relatively better agreement with experiment that we find here may stem from our use of an all-atom model for hexane. Melting. To study the melting of a pentane ML, we performed MD simulations at temperatures ranging from 0 to 250 K. In these simulations, we began with our zerotemperature ML structures and raised the temperature to 20 K. At this temperature, we performed an equilibration run for 500 ps and a production run for 500 ps to obtain statistics of the ML. Subsequently, we raised the temperature by 20 K and repeated the cycle of equilibration and production. We continued this cycle of heating, taking the equilibrated structure from a lower temperature as the initial structure for the higher temperature, in increments of 20, 10, or 5 K, until we reached a temperature of 250 K. Although the potential energy reached a constant value by the end of each equilibration run and maintained that value throughout the subsequent production run, it is possible that longer equilibration times were necessary because of very slow transients for some of the runs at the lowest temperatures. We calculated three different quantities to characterize the melting of the layers: the average potential energy, the structural (OP2), nematic (OPn), and (in the case of hexane) herringbone (HB) (OPh) order parameters, and the in-plane radial distribution function of the molecular center of mass g(r). The structural order parameter is defined as
Figure 2. Definition of the three angles specifying the molecular orientation in a coordinate system fixed to the graphite substrate. The z axis is perpendicular to the graphite basal plane, and the directions of the x and y axes are defined in Figure 1. The long axis of the molecule is indicated by the dashed line. The orientation of the long axis is specified by the polar angle Θ and azimuthal angle Φ. The rolling angle Ψ describes rotation about the long axis.
tion.16,19,20,25 The polar angle Θ is the angle between the long axis of the molecule and the z direction perpendicular to the surface, and the in-plane azimuthal angle Φ gives the direction of the molecular long axis in the xy plane. The long axis is defined to be the principal axis of the molecule with the smallest moment of inertia. When the molecule is in the trans conformation, the principal axis with the largest moment of inertia is perpendicular to the plane of the carbon backbone. The rolling angle Ψ is the angle between this axis and the surface plane so that ψ = 90° when the backbone plane is parallel to the surface for an all-trans alkane. Our calculated structural parameters for the unit cells of both molecules are compared with values obtained from neutron diffraction experiments20,23−25 in Tables 2 and 3. Here, we see that our calculated lattice parameters are in close agreement with those from experiments. Using a united-atom model, Hansen and Taub16,21 also tested the structural parameters of the hexane
OP2 =
1 N
N
∑ cos(2Φi) (16)
i=1
Table 2. Comparison of Experimental Lattice Values to Those Calculated in This Study for the Pentane ML at Zero Temperaturea 1
2
lattice
parameter
calc
expt25
calc
expt25
x/Å y/Å Ψ/deg Θ/deg Φ/deg a/Å b/Å
0.00 0.00 89.9 0.0 0.0
0.00 0.00 90.0 0.0 0.0 ± 5.0
2.13 8.61 89.9 0.0 0.0
2.34 8.51 90.0 0.0 0.0 ± 5.0
calc
expt25
expt23
4.26 17.22
4.67 ± 0.02 17.01 ± 0.02
4.26 17.1
a
1 and 2 represent the two molecules in the unit cell (cf. Figure 1a). x and y denote center-of-mass coordinates. The lattice constants (a, b) and angles (Ψ, Θ, Φ) are defined in Figures 1 and 2, respectively. 7385
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Figure 3. Evolution of (a) the potential energy, (b) OP2 and OPn, and (c) g(r) for the pentane ML as a function of temperature.
Figure 4. Snapshots of pentane MLs at (a) 0, (b) 150, and (c) 155 K. Carbons are green, and hydrogens are white.
where the four-quadrant version of tan−1 is used. The nematic order parameter quantifies the tendency of the molecular axes to be aligned in one direction and takes on nonzero values when significant alignment occurs. The HB order parameter is given by
where N is the number of molecules, Φi is the azimuthal angle that the long axis of molecule i makes with the x axis of the graphite cell (Figure 2), and ⟨···⟩ denotes an ensemble average. This order parameter indicates the existence of 2-fold symmetry in the solid phase. For an ordered phase, OP2 is nonzero and assumes values close to zero when the system loses order. The nematic order parameter is defined as OPn =
1 N
OPh =
N
(17)
where Φi is defined above. The director Φdir is defined as Φdir =
⎡ ∑N sin(2Φ ) ⎤ 1 i ⎥ tan−1⎢ Ni = 1 ⎢⎣ ∑ cos(2Φi) ⎥⎦ 2 i=1
N
∑ (−1) j sin(2Φi) (19)
i=1
where Φi is defined above. The integer j is set to account for different sublattices of the HB pattern. The HB order parameter assumes high values when the system exhibits HB ordering and zero values when this type of ordering does not occur. The in-plane radial distribution function is defined as
∑ cos(2(Φi − Φdir)) i=1
1 N
g (r ) = (18) 7386
N (r , r + Δr ) 2πr Δrρ
(20)
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Figure 5. Evolution of (a) the potential energy, (b) OP2, OPn, and OPh, and (c) g(r) for the hexane ML as a function of temperature. The inset in c shows a blow-up of the region between 0 and 2 Å.
Figure 6. Snapshots of hexane MLs at (a) 0, (b) 180, and (c) 185 K. Carbons are green, and hydrogens are white.
where N(r, r + Δr) is the number of molecules whose centerof-mass coordinates in the surface plane are between r and r + Δr from those of a fixed molecule and ρ is the 2D center-ofmass density. Errors in calculated quantities Δx were estimated using
⎡ ∑No (x − x)̂ 2 ⎤1/2 i ⎥ Δx = ⎢ i = 1 ⎢⎣ No(No − 1) ⎥⎦
7387
(21)
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Figure 7. MD snapshots illustrating the second-layer promotion mechanism of melting in a hexane ML at 180 K. In the initial configuration (a), all of the molecules are arranged in a well-ordered HB structure. (b) Two of the molecules (shown with larger green carbons and blue hydrogens) hop above the first layer, leaving space for two neighboring molecules (shown with larger blue carbons and red hydrogens) to disorder in the resulting vacancy.
where No is the number of observations, x̂ is the mean value of x, and xi is the value of x at step i. We calculated averages and the error in all quantities at a time interval of 5 ps. In all cases, we find that the error bars are smaller than our symbol sizes. Pentane. In Figure 3, we characterize the melting of the pentane ML. Figure 3a shows the potential energy as a function of temperature. A jump in the energy between 150 and 155 K indicates that a phase transition occurs in this temperature range. Figure 3b shows OP2 and OPn as a function of temperature. Both order parameters exhibit values near unity below 150 K, indicating the prevalence of the low-temperature RC structure. There is a profound loss of order in the system between 150 and 155 K associated with melting in this temperature range. In Figure 3c, we show g(r) for pentane ML at various temperatures. At temperatures of 150 K and below, g(r) exhibits many peaks that are characteristic of a solid. When the temperature is 155 K or above, the peaks in g(r) vanish beyond r ≈ 5 Å and g(r) converges to unity at large r, which is characteristic of a liquid. Thus, the potential energy, order parameters, and radial distribution function all indicate a melting transition between 150 and 155 K. Typical configurations of the pentane layer at various temperatures are shown in Figure 4, which also indicates a melting transition from an ordered phase to a disordered phase between 150 and 155 K. The melting temperature that we find for the pentane ML agrees with that found by Pint,13 who used an anisotropic united-atom model (AUA4) to model pentane overlayers in MD simulations of (near) ML melting. We also agree with the experimental results of Castro et al.,22 who used neutron diffraction to probe the melting of pentane layers adsorbed on graphite at the solid−liquid interface and found a melting temperature of 150 K. Our simulations indicate an abrupt melting transition (Figure 3), consistent with experiment.22 We note that both simulations13 and experiments22,25 indicate that the melting behavior of a pentane ML is sensitive to surface coverage: the melting temperature is lower for lower coverages. Thus, our results do not match those of Kruchten et al.,25
whose experiments probed a somewhat lower coverage and found a lower melting temperature than ours. Hexane. The hexane ML simulations were performed at temperatures between 0 and 260 K, in an analogous way to those for pentane. In Figure 5, we show the potential energy, order parameters, and in-plane radial distribution function as a function of temperature. We see discontinuous jumps in the potential energy and the order parameters between 180 and 185 K in Figure 5a,b, indicative of a melting transition. In addition, g(r) exhibits solidlike peaks at 180 K, which have vanished at in-plane separations greater than ∼4 Å by 185 K, also pointing to a transition from a solidlike to a liquidlike structure between 180 and 185 K. Typical configurations of the hexane layer at various temperatures are shown in Figure 6, which also indicates the transition from an ordered phase to a disordered phase as the temperature increases from 180 to 185 K. Comparing this result to the experimental value of 175 K from neutron diffraction,19−21 we find a discrepancy of ∼4.3%. In a recent study, Wexler et al.11 also probed the melting of a hexane ML in MD simulations based on the CHARMM22 allatom force field. Although our model is different from theirs, as we will elaborate on below, our results are similar to theirs in several respects. First, we find that the hexane ML has a direct melting transition from an HB structure to a liquid, as they found.11 There is no evidence of the nematic mesophase observed in previous MD studies of (near) ML hexane melting.14−17 We also confirm the general melting pathway that they found, in which RC domains form and grow in size at temperatures approaching the melting temperature. Figure 5b indicates that both OP2 and OPn increase slightly as the temperature increases toward melting, consistent with the formation of small nematic domains. Subsequent to melting, Wexler and colleagues observed that the RC domains decrease in size with increasing temperature.11 Instead of observing this decrease, we observe that OPn increases to a peak value and begins to decrease immediately prior to melting (Figure 5b). Subsequent to melting, OPn reaches a constant plateau value of ∼0.1, indicating residual nematic order. The MD snapshot shown in Figure 6c subsequent to melting indicates the 7388
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presence of small, residual nematic domains in which neighboring molecules have their long axes aligned in the RC structure. This melting scenario is consistent with experimental scattering studies.19−21 Mechanisms of Melting. To elucidate the detailed melting mechanisms in these systems, we analyzed the temperature dependence of gauche defects and the tilting angle Θ (cf. Figure 2) between the long axis of the molecule and the surface. These quantities have been proposed to contribute to the footprintreduction mechanism of melting whereby a molecule creates vacancies in the layer by tilting away from the surface and/or forming gauche defects.21 Vacancies formed by footprint reduction facilitate disordering of the layer and hence promote melting. We note that evidence for footprint reduction has been observed in previous MD studies of melting in alkane layers.11−13,15,16,21 In our study, we observe a qualitatively different mechanism in which molecules tend to jump to the second layer, remain there for a brief time, and then re-enter the first layer in a second-layer promotion mechanism that leaves vacancies in the first layer. Figure 7 shows a sequence of MD snapshots illustrating this mechanism. Because these vacancies free up space for first-layer molecules to disorder, they also facilitate melting. We note that the role of secondlayer promotion in the melting transition was first discussed by Abraham in his MD studies of the melting of Xe on graphite.36 To assess the importance of second-layer promotion in facilitating melting, we also analyze the fraction of the total number of molecules in the second layer as a function of temperature. In this analysis, a molecule is considered to be in the second layer if the height of all of its atoms is above the average height of the ML. Pentane. In Figure 8a, we plot the fraction of pentane molecules in the second layer along with the fraction containing one or more gauche defects as a function of temperature. Here, we see that the fraction of molecules with gauche defects remains constant at its low-temperature value throughout the melting window and begins to increase only subsequent to melting. This indicates that there is little connection between gauche defects and melting for pentane. The fraction of molecules in the second layer exhibits a more substantial increase from a near-zero value at and below the beginning of the melting window (150 K) to 4.4% at the end of the melting window (155 K). Figure 8b shows the fraction of pentane molecules with various tilt angles. Unlike the fraction in the second layer, the fraction of molecules with a tilt angle greater than Θ increases continuously with increasing temperature up to the beginning of the melting window, where it exhibits a discontinuous jump. The magnitude of the jump from the beginning to the end of the melting window ranges from 4.3% for Θ ≥ 5° to 5.1% for Θ ≥ 20°. Thus, both tilting (which leads to footprint reduction) and second-layer promotion play a role in the melting of the pentane ML. Hexane. The fractions of gauche defects, second-layer molecules, and molecules with tilt angles greater than Θ are shown as a function of temperature for the hexane ML in Figure 9. In Figure 9a, we see that the fractions of gauche defects and second-layer molecules both exhibit discontinuous jumps around the melting window. At 2.3%, the increase in the fraction of molecules with gauche defects is larger for hexane than it is for pentane. However, the increase is still relatively small. The jump in the fraction of second-layer hexane molecules from near zero prior to melting to 9.5% at the end of the melting window is dramatic and indicates that second-
Figure 8. Indicators of the melting mechanism for the pentane ML. (a) Fraction of molecules with at least one gauche defect and fraction of molecules that reside in the second layer as a function of temperature. (b) Fraction of molecules with tilt angles greater than or equal to Θ for various values of Θ as a function of temperature. The dashed-dotted lines indicate the temperature window over which melting occurs.
layer promotion plays a significant role in the melting of the hexane ML. Evidence for second-layer molecules can also be seen in the in-plane radial distribution function for hexane in the inset of Figure 5c. Here, we see that g(r) is slightly greater than zero when r is smaller than ∼1.7 Å at 185 K and above but negligible at 180 K and below. Because the in-plane radial distribution function is calculated in the two orthogonal directions parallel to the surface, the only way for two molecules to be this close without overlapping is by residing in two different layers. Similar to pentane, the fraction of molecules with a tilt angle greater than Θ increases continuously with increasing temperature up to the beginning of the melting window, where it exhibits a discontinuous jump (Figure 9b). The magnitude of the jump from the beginning to the end of the melting window ranges from 4% for Θ ≥ 5° to 2% for Θ ≥ 20°. Thus, similar to pentane, both tilting and second-layer promotion play a role in the melting of hexane ML. In the case of hexane, we find that the role of second-layer promotion is significant and this finding appears to be unique to our study.
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DISCUSSION Thus, we characterized melting in MD studies of two model systems representing pentane and hexane ML adsorbed on the basal plane of graphite. The trends that we observe here are consistent with experimental studies19−24 as well as with the most recent MD studies for pentane13 and hexane.11 However, the underlying mechanisms of melting appear to be unique to 7389
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in previous MD studies, which demonstrated that the melting transition could be pushed to higher temperatures by altering the torsion potential to inhibit the formation of gauche defects.13,21 Connolly et al.12 used the CHARMM22 all-atom force field to study the melting of hexane layers and found that the appearance of the nematic mesophase prior to melting was linked to the formation of gauche defects. In their study, Wexler and colleagues altered the molecular flexibility by changing the f jk factor in eq 5 (for 1−4 pairs) from the commonly used value of f14 = 0.5 (the value that we use here) to a value of f14 = 0.8. This also inhibits the formation of gauche defects because larger values of the scaling factor lead to the suppression of gauche defects until higher temperatures are reached.18 We note that changing the value of f14 will also alter the properties of fluid-phase hexane because the CHARMM22 potential was fit by assuming f14 = 0.5. Here, we do not observe a significant fraction of molecules with gauche defects until temperatures higher than the melting window are reached. This is due to differences in the parametrization of the CHARM22 and OPLS-AA force fields: The CHARMM22 force field tends to underestimate torsional barriers and energies for gauche conformers of hexane compared to ab initio values,37 whereas the OPLS-AA force field tends to overestimate these values.38,39 When torsion is inhibited, gauche defects play a smaller role in footprint reduction. Here, they play no role for pentane and only a small role for hexane. Another significant (and apparently unique) factor contributing to the success of our model is that the alkane−surface interaction is weaker than in previous models.11−18 Velasco and Peters pointed out that the molecule−surface interaction could play a profound role in dictating the melting temperature in hexane ML on graphite,17 although the lowest value that they considered for εC (which governs the alkane−surface interaction) is larger than our value. In a previous study,26 we used our model to simulate the temperature-programmed desorption (TPD) of pentane from the basal plane of graphite, and our simulated spectrum for a pentane ML agrees well with experiment,40,41 with a discrepancy in the peak temperature of ∼1°. TPD is the most common way to assess the binding energy of a molecule to a solid surface experimentally, so matching the TPD spectrum is a strong indication that we are accurately capturing the alkane binding strength. One aspect to emphasize in our studies of alkane desorption26−28 is the important role of alkane−alkane interactions in determining the overall binding energy of an alkane molecule to a solid surface. Assuming εCG = 0.291 kJ/ mol and εHG = 0.214 kJ/mol for the interaction of C and H atoms in the alkane with atoms in the graphite surface (close to the values used by Wexler and co-workers11), we were able to match various simulated n-alkane binding energies for the desorption of single molecules to experimental binding energies obtained at near-monolayer coverage.27 In single-molecule simulations, there are no intermolecular interactions, and a larger molecule−surface interaction was needed to mimic this attraction. However, when we simulated desorption from a pentane ML, we found that these values for the molecule− surface interaction were too high and we needed to use the present values to match experimental TPD spectra.26 With a weaker molecule−surface interaction, the relative importance of the molecule−molecule interaction increases, allowing secondlayer promotion to occur at temperatures around the melting window. The vacancies created by second-layer molecules allow the layer to disorder so that melting occurs.
Figure 9. Indicators of the melting mechanism for the hexane ML. (a) Fraction of molecules with at least one gauche defect and fraction of molecules that reside in the second layer as a function of temperature. (b) Fraction of molecules with tilt angles greater than or equal to Θ for various values of Θ as a function of temperature. The dashed-dotted lines indicate the temperature window over which melting occurs.
our study. We observe melting trends similar to those observed by Pint,13 who adopted the AUA4 model for pentane chains. We also appear to confirm the trend in that study that molecular flexibility (i.e., the formation of gauche defects) does not contribute to the melting of pentane. Instead, we find that the tilting of the molecules away from the surface and the promotion of a small fraction of the molecules to the second layer are what appear to facilitate melting. The study by Wexler and colleagues11 was apparently the first in a long line of MD studies12,14,15,17,21 that was successful at resolving the major experimentally observed features in the melting of hexane ML on graphite. We are approximately equally successful at describing the melting transition, although the melting temperature that we find is about 5−10° higher than in the experiment. The claim in the Wexler study is that achieving zero spreading pressure in the simulation, by correct choice of the hexane unit cell, is important in securing agreement with experiment. We note that the unit cell that we determined for the hexane ML (Table 3) is in excellent agreement with experiment and has a somewhat lower area per molecule (41.92 Å2/molecule) than theirs (45.14 Å 2/ molecule).11 We note that both simulations13 and experiments22,25 indicate that the melting behavior of a pentane ML is sensitive to surface coverage: the melting temperature is lower for lower coverages. Thus, it is possible that we could have achieved a lower melting temperature by adopting a larger unit cell for hexane. However, such a cell would not provide the minimum-energy structure for the present potential. A second feature important in achieving the correct melting temperature is molecular flexibility. Molecular flexibility was shown to be important in influencing the melting temperature 7390
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(2) Dimitrakopoulos, C. D.; Malenfant, P. R. L. Organic Thin Film Transistors for Large Area Electronics. Adv. Mater. 2002, 14, 99−117. (3) Peumans, P.; Yakimov, A.; Forrest, S. R. Small Molecular Weight Organic Thin-Film Photodetectors and Solar Cells. J. Appl. Phys. 2003, 93, 3693−3723. (4) Djuric, T.; Ules, T.; Gusenleitner, S.; Kayunkid, N.; Plank, H.; Hlawacek, G.; Teichert, C.; Brinkmann, M.; Ramsey, M.; Resel, R. Substrate Selected Polymorphism of Epitaxially Aligned TetraphenylPorphyrin Thin Films. Phys. Chem. Chem. Phys. 2012, 14, 262−272. (5) Muccioli, L.; D’Avino, G.; Zannoni, C. Simulation of Vapor-Phase Deposition and Growth of a Pentacene Thin Film on C60 (001). Adv. Mater. 2011, 23, 4532−4536. (6) Beljonne, D.; Cornil, J.; Muccioli, L.; Zannoni, C.; Brédas, J. L.; Castet, F. Electronic Processes at Organic-Organic Interfaces: Insight from Modeling and Implications for Opto-electronic Devices. Chem. Mater. 2011, 23, 591−609. (7) Chang, J.; Sandler, S. I. Free Energy of the Solid C60 Fullerene Orientational Order-Disorder Transition. J. Chem. Phys. 2006, 125, 054705. (8) Clancy, P. Application of Molecular Simulation Techniques to the Study of Factors Affecting the Thin-Film Morphology of SmallMolecule Organic Semiconductors. Chem. Mater. 2011, 23, 522−543. (9) Delle Valle, R. G.; Venuti, E.; Brillante, A.; Girlando, A. Molecular Dynamics Simulations for a Pentacene Monolayer on Amorphous Silica. Chem. Phys. Chem. 2009, 10, 1783−1788. (10) Mansfeld, S. C. B.; Fritz, T. Advanced Modelling of Epitaxial Ordering of Organic Layers on Crystalline Surfaces. Mod. Phys. Lett. B 2006, 20, 585−605. (11) Wexler, C.; Firlej, L.; Kuchta, B.; Roth, M. W. Melting of Hexane Monolayers Adsorbed on Graphite: The Role of Domains and Defect Formation. Langmuir 2009, 25, 6596−6598. (12) Connolly, A. J.; Roth, M. W.; Gray, P. A.; Wexler, C. Explicit Hydrogen Molecular Dynamics Simulations of Hexane Deposited onto Graphite at Various Coverages. Langmuir 2008, 24, 3228−3234. (13) Pint, C. L. Different Melting Behavior in Pentane and Heptane Monolayers on Graphite: Molecular Dynamics Simulations. Phys. Rev. B 2006, 73, 045415. (14) Pint, C. L.; Roth, M. W.; Wexler, C. Behavior of Hexane on Graphite at Near-Monolayer Densities: Molecular Dynamics Study. Phys. Rev. B 2006, 73, 085422. (15) Roth, M. W.; Pint, C. L.; Wexler, C. Phase Transitions in Hexane Monolayers Physisorbed onto Graphite. Phys. Rev. B 2005, 71, 155427. (16) Hansen, F. Y.; Newton, J. C.; Taub, H. Molecular-Dynamics Studies of the Melting of Butane and Hexane Monolayers Adsorbed on the Basal-Plane Surface of Graphite. J. Chem. Phys. 1993, 98, 4128− 4141. (17) Velasco, E.; Peters, G. H. Effect of Substrate Potential Strength on the Melting Temperature of a Hexane Monolayer Adsorbed on Graphite. J. Chem. Phys. 1995, 102, 1098−1099. (18) Firlej, L.; Kuchta, B.; Roth, M. W.; Wexler, C. Molecular Simulations of Intermediate and Long Alkanes Adsorbed on Graphite: Tuning of Non-Bond Interactions. J. Mol. Model. 2011, 17, 811−816. (19) Krim, J.; Suzanne, J.; Shechter, H.; Wang, R.; Taub, H. A Leed and Neutron-Diffraction Study of Hexane Adsorbed on Graphite in the Monolayer Range - Uniaxial Commensurate Incommensurate Transition. Surf. Sci. 1985, 162, 446−451. (20) Newton, J. C. Ph.D. Dissertation. University of Missouri Columbia, 1989. (21) Hansen, F. Y.; Taub, H. Melting Mechanism in Monolayers of Flexible Rod-Shaped Molecules. Phys. Rev. Lett. 1992, 69, 652−655. (22) Castro, M. A.; Clarke, S. M.; Inaba, A.; Arnold, T.; Thomas, R. K. Anomalous Behaviour of Pentane Adsorbed at the Graphite/Liquid Interface. Phys. Chem. Chem. Phys. 1999, 1, 5203−5207. (23) Arnold, T.; Dong, C. C.; Thomas, R. K.; Castro, M. A.; Perdigon, A; Clarke, S. M.; Inaba, A. The Crystalline Structures of the Odd Alkanes Pentane, Heptane, Nonane, Undecane, Tridecane And Pentadecane Monolayers Adsorbed on Graphite at Submonolayer
CONCLUSIONS We presented a model for the adsorption of pentane and hexane on the basal plane of graphite, and we used MD simulations based on this model to probe the melting of pentane and hexane MLs. For both of these molecules, we achieve good agreement with experimental studies on all measured aspects of melting. A second feature of our model is that it can reproduce experimental TPD spectra for pentane desorption from graphite.26 We emphasize that two features of our model appear to be unique. First, the alkane−surface interaction is weaker in our study than in previous studies. This weaker interaction leads to the promotion of a small fraction of molecules into the second layer at temperatures in the melting window. The vacancies created by second-layer molecules allow the first layer to disorder so that melting occurs. A second unique feature of our model is that we employ the OPLS-AA force field to describe inter- and intramolecular alkane interactions. Apparently, the energies for gauche states are higher in this model than those in previous studies of alkane melting so that gauche defects play no role in the melting transition of pentane and only a small role in the melting of hexane. This leads to an abrupt HB → liquid transition, where small nematic domains appear and grow prior to melting and then persist in the midst of a disordered liquidlike phase subsequent to melting. In addition to secondlayer promotion, we observe a jump in the out-of-plane tilting of the long axes of both molecules over their melting windows. By tilting away from the surface, a molecule reduces its footprint in the layer and creates free space for melting. Thus, our results indicate that a combination of footprint reduction and second-layer promotion underlies melting in these systems. Another point that arises in this study is that the melting in these systems arises from an intricate combination of interactions, and by comparing our study with those of Pint13 and Wexler and colleagues,11 we see that this combination is not unique. This indicates that to achieve a firm understanding of the structure and function of organic thin films, a holistic view is needed, with a focus that is broader than a single experimental measure. Here, we match the low-temperature unit cell inferred from experimental scattering studies, the melting temperature, and the molecule−surface interaction revealed in experimental TPD studies. Such an approach will ultimately be useful in designing organic thin-film structures.
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AUTHOR INFORMATION
Corresponding Author
*E-mail: fi
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We acknowledge useful discussions with Flemming Hansen, Maria Mignogna, Yogesh Tiwary, and Yangzheng Lin. This research was supported by the National Science Foundation (grants DGE 9987589 and DMR 0514336) and the China Scholarship Council.
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